Math: Building sideboards for stairs

[Prototype]

OK, so I'm trying to cut sideboards for the stairs I'm trying to build. I need to figure out the short side measurement.

The height to the top of the deck is 29 inches.
The long side of the side panel is going to go out 3 feet (36 inches)
Using a2 + b2 = c2, I have figured the diagonal of the triangle to be 46.25 inches.
The width of the board is 9.25 inches.
Trying to figure out the short side so I can measure that out, and make my cuts so that the one side is flush with the deck, and the other is flush with the ground.

Any ideas?

[GreenTeaFrapp]

Subtract 9.25 from each side and use the Pythagorean theorem again to calculate the length.

[Boo Radley]

31.48 inches

[Prototype]

Originally Posted by GreenTeaFrapp

Subtract 9.25 from each side and use the Pythagorean theorem again to calculate the length.

I had thought about that, but the cut is going to be longer that 9.25, right?

[Prototype]

Originally Posted by Boo Radley

31.48 inches

Can you explain, so I don't jump into cutting... again...

[Boo Radley]

Yes, give me a second

[jayswin]

Have you tried using pie?

[awildermode]

it is about 27.425

i used Illustrator and created your triangle. then a 9.25 plank...measured it and got that.

your smaller triangle is about 17 X 21.5

[Boo Radley]

1. Calculate the lower right angle to be 38.85. inverse tan of 29/36.

2. Construct smaller triangle in lower right using angle 38.85 and opposite length of 9.25 to determine an adjacent side length of 11.484 inches.

3. Determine the two sides of your smaller triangle: a) subtract 9.25 in from 29 to get 19.75 inches b) subtract 11.484 inches from 36 to get 24.516 inches

4) Sides of your smaller triangle are 19.75 in and 24.516 inches.
Use pythagorean theorem to get your missing length of 31.48 inches.

If that is incorrect i will come over and and help and bring the beer!

Radley

[RatherDashing]

31.48, Boo has it right. The bottom dimension will be 24.52 inches.

Edit-What Boo said.

[awildermode]

^uh, at least one of us is wrong

[Prototype]

Originally Posted by flameswin

Have you tried using pie?

I usually use apple in this sort of situation, but sometimes blueberry is best.

[metallicat]

*head explodes*

[awildermode]

Prototype:

I am not sure which one is right. I just redid the thing on Illustrator and got the same results. I hope I did not derail your progress in your construction, sorry if I did.

Good luck.

[Prototype]

Question for awilder and boo... are either of you using the 9.25 as the width as shown in the picture. When it's not cut, it's 9.25. The width is more on a diagnol <sp?>, not the way it's shown... if that makes any sense...

[Boo Radley]

Do not cut yet I am re-checking my calculations. From your drawing I think I miss read the width. I will double check

[awildermode]

Originally Posted by Prototype

Question for awilder and boo... are either of you using the 9.25 as the width as shown in the picture. When it's not cut, it's 9.25. The width is more on a diagnol <sp?>, not the way it's shown... if that makes any sense...

Oh, that changes everything. if the board is 9.25 in vertical measurement, meaning the actual width of the board is about 7.3

then yes, boo is correct. measurement is about 31.475 short side is 19.75 base of about 24.6

[Prototype]

The board is originally 10 feet long, 9.25 inches wide, and about 1.5 inches thick.

The length to cut is what I'm looking for, and the thickness shouldn't play in this equation.

Here goes nothing.

[Boo Radley]

So when I re-do the calculations using an un-cut board width of 9.25 inches.
I calculate your missing length to be 27.29 inches.

The confusion is in the width. If the width at an angle of 90 measures 9.25 inches then the length should be 27.29 inches. From your drawing I thought the 9.25 inches was measured at the diagonal.

I guess I will be over with the Beer

[awildermode]

I guess i was right the first time. Boo and his silly math is no match for my mad illustrator skills